which graph is the sequence defined by the function f(x) = 3(2)^(x - 1)?
which graph is the sequence defined by the function f(x) = 3(2)^(x - 1)?
Answer
Explanation:
Step1: Find values of the sequence for different x - values
When (x = 1), (f(1)=3(2)^{1 - 1}=3(2)^{0}=3\times1 = 3). When (x = 2), (f(2)=3(2)^{2 - 1}=3\times2^{1}=3\times2 = 6). When (x = 3), (f(3)=3(2)^{3 - 1}=3\times2^{2}=3\times4 = 12). When (x = 4), (f(4)=3(2)^{4 - 1}=3\times2^{3}=3\times8 = 24).
Step2: Check the points on the given graphs
The points ((1,3)), ((2,6)), ((3,12)), ((4,24)) should be on the correct graph. Analyzing the given graph, we can see that the points on the graph do not match the values we calculated from the function (f(x)=3(2)^{x - 1}). For example, in the given graph, when (x = 1), (y = 6) instead of (y = 3) as per our calculation. So, the given graph is not the graph of the sequence defined by (f(x)=3(2)^{x - 1}). But if we assume we need to find the correct - shaped graph for the exponential - type sequence: The general form of an exponential function is (y = a\cdot b^{x - 1}), where (a = 3) and (b = 2). The function (y = 3(2)^{x - 1}) is an exponential growth function. The (y) - values will increase rapidly as (x) increases. The initial value (when (x = 1)) is (y = 3), and then it doubles for each increase in (x) by 1.
Answer:
The graph should have points ((1,3)), ((2,6)), ((3,12)), ((4,24)) etc. and show exponential growth. Since the given graph does not match these points, it is not the correct graph for (f(x)=3(2)^{x - 1}).